What is the integral from 1 to 2 of (3x^3+2)/(x^3) ?

The integral from 1 to 2 of (3x^3+2)/(x^3) is 15/4

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integral from 1 to 2 of (3x^3+2)/(x^3)

\int_{1}^{2} \frac{3 x ^{3} + 2}{x ^{3}} d x

\frac{15}{4}

Decimal

3.75

Solution steps

\int_{1}^{2} \frac{3 x ^{3} + 2}{x ^{3}} d x

Expand

\frac{3 x ^{3} + 2}{x ^{3}} : 3 + \frac{2}{x ^{3}}

= \int_{1}^{2} 3 + \frac{2}{x ^{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} 3 d x + \int_{1}^{2} \frac{2}{x ^{3}} d x

\int_{1}^{2} 3 d x = 3

\int_{1}^{2} \frac{2}{x ^{3}} d x = \frac{3}{4}

= 3 + \frac{3}{4}

Simplify

3 + \frac{3}{4} : \frac{15}{4}

= \frac{15}{4}

What is the integral from 1 to 2 of (3x^3+2)/(x^3) ?
The integral from 1 to 2 of (3x^3+2)/(x^3) is 15/4